The goal of this project is to reconsider core market and reliability processes that can potentially yield to transformative advances in power grid security, reliability, and efficiency. Current electric power market designs are strongly a function of computing capabilities and limitations that were available in the mid-to-late 1990s, circa deregulation. This includes constructs such as: (1) a 2-tiered day-ahead/real-time market construct; and (2) linearized (“DC”) real power flow approximations in dispatch and pricing. At that time, state-of-the-art computational capabilities could at the limit address deterministic mixed-integer programming formulations of unit commitment (UC) and linear programming formulations of economic dispatch (ED) at limited fidelity and scale. Such constraints forced limited look-ahead time-horizons, crude approximations of AC power flow physics and operations, and artificial partitioning between day-ahead markets, hour(s)-ahead reliability processes, and real-time markets. Consequently, these limitations have resulted in limited security and reliability with increasing out-of-market payments, particularly as uncertainty associated with renewables and distributed energy resources grows.
In this paper we report preliminary results from the novel coupling of cyber-physical emulation and interdiction optimization to better understand the impact of a CrashOverride malware attack on a notional electric system. We conduct cyber experiments where CrashOverride issues commands to remote terminal units (RTUs) that are controlling substations within a power control area. We identify worst-case loss of load outcomes with cyber interdiction optimization; the proposed approach is a bilevel formulation that incorporates RTU mappings to controllable loads, transmission lines, and generators in the upper-level (attacker model), and a DC optimal power flow (DCOPF) in the lower-level (defender model). Overall, our preliminary results indicate that the interdiction optimization can guide the design of experiments instead of performing a 'full factorial' approach. Likewise, for systems where there are important dependencies between SCADA/ICS controls and power grid operations, the cyber-physical emulations should drive improved parameterization and surrogate models that are applied in scalable optimization techniques.
Securing cyber systems is of paramount importance, but rigorous, evidence-based techniques to support decision makers for high-consequence decisions have been missing. The need for bringing rigor into cybersecurity is well-recognized, but little progress has been made over the last decades. We introduce a new project, SECURE, that aims to bring more rigor into cyber experimentation. The core idea is to follow the footsteps of computational science and engineering and expand similar capabilities to support rigorous cyber experimentation. In this paper, we review the cyber experimentation process, present the research areas that underlie our effort, discuss the underlying research challenges, and report on our progress to date. This paper is based on work in progress, and we expect to have more complete results for the conference.
While peak shaving is commonly used to reduce power costs, chemical process facilities that can reduce power consumption on demand during emergencies (e.g., extreme weather events) bring additional value through improved resilience. For process facilities to effectively negotiate demand response (DR) contracts and make investment decisions regarding flexibility, they need to quantify their additional value to the grid. We present a grid-centric mixed-integer stochastic programming framework to determine the value of DR for improving grid resilience in place of capital investments that can be cost prohibitive for system operators. We formulate problems using both a linear approximation and a nonlinear alternating current power flow model. Our numerical results with both models demonstrate that DR can be used to reduce the capital investment necessary for resilience, increasing the value that chemical process facilities bring through DR. However, the linearized model often underestimates the amount of DR needed in our case studies. Published 2018. This article is a U.S. Government work and is in the public domain in the USA. AIChE J, 65: e16508, 2019.
While the concept of aggregating and controlling renewable distributed energy resources (DERs) to provide grid services is not new, increasing policy support of DER market participation has driven research and development in algorithms to pool DERs for economically viable market participation. Sandia National Laboratories recently undertook a 3 year research programme to create the components of a real-world virtual power plant (VPP) that can simultaneously participate in multiple markets. The authors' research extends current state-of-the-art rolling horizon control through the application of stochastic programming with risk aversion at various time resolutions. Their rolling horizon control consists of day-ahead optimisation to produce an hourly aggregate schedule for the VPP operator and sub-hourly optimisation for the real-time dispatch of each VPP subresource. Both optimisation routines leverage a two-stage stochastic programme with risk aversion and integrate the most up-to-date forecasts to generate probabilistic scenarios in real operating time. Their results demonstrate the benefits to the VPP operator of constructing a stochastic solution regardless of the weather. In more extreme weather, applying risk optimisation strategies can dramatically increase the financial viability of the VPP. The methodologies presented here can be further tailored for optimal control of any VPP asset fleet and its operational requirements.
We propose a novel global solution algorithm for the network-constrained unit commitment problem that incorporates a nonlinear alternating current (ac) model of the transmission network, which is a nonconvex mixed-integer nonlinear programming problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. We exploit the mathematical structure of the unit commitment problem with ac power flow constraints and leverage second-order cone relaxations, piecewise outer approximations, and optimization-based bounds tightening to provide a globally optimal solution at convergence. Numerical results on four benchmark problems illustrate the effectiveness of our algorithm, both in terms of convergence rate and solution quality.
This paper proposes a dc optimal power flow (DCOPF) with losses formulation (the ℓ-DCOPF + S problem) and uses it to investigate the role of real power losses in OPF-based grid-scale storage integration. We derive the ℓ-DCOPF + S problem by augmenting a standard DCOPF with storage (DCOPF + S) model to include quadratic real power loss approximations. This procedure leads to a multiperiod nonconvex quadratically constrained quadratic program, which we prove can be solved to optimality using either a semidefinite or second-order cone relaxation. Our approach has some important benefits over existing models. It is more computationally tractable than ACOPF with storage (ACOPF + S) formulations and the provably exact convex relaxations guarantee that an optimal solution can be attained for a feasible problem. Adding loss approximations to a DCOPF + S model also leads to a more accurate representation of locational marginal prices, which have been shown to be critical in determining optimal storage dispatch and siting in prior ACOPF + S-based studies. Case studies demonstrate the improved accuracy of the ℓ-DCOPF + S model over a DCOPF + S model and the computational advantages over an ACOPF + S formulation.
Electricity markets rely on the rapid solution of the optimal power flow (OPF) problem to determine generator power levels and set nodal prices. Traditionally, the OPF problem has been formulated using linearized, approximate models, ignoring nonlinear alternating current (AC) physics. These approaches do not guarantee global optimality or even feasibility in the real ACOPF problem. We introduce an outer-approximation approach to solve the ACOPF problem to global optimality based on alternating solution of upper- and lower-bounding problems. The lower-bounding problem is a piecewise relaxation based on strong second-order cone relaxations of the ACOPF, and these piecewise relaxations are selectively refined at each major iteration through increased variable domain partitioning. Our approach is able to efficiently solve all but one of the test cases considered to an optimality gap below 0.1%. Furthermore, this approach opens the door for global solution of MINLP problems with AC power flow equations.
The solution of the Optimal Power Flow (OPF) and Unit Commitment (UC) problems (i.e., determining generator schedules and set points that satisfy demands) is critical for efficient and reliable operation of the electricity grid. For computational efficiency, the alternating current OPF (ACOPF) problem is usually formulated with a linearized transmission model, often referred to as the DCOPF problem. However, these linear approximations do not guarantee global optimality or even feasibility for the true nonlinear alternating current (AC) system. Nonlinear AC power flow models can and should be used to improve model fidelity, but successful global solution of problems with these models requires the availability of strong relaxations of the AC optimal power flow constraints. In this paper, we use McCormick envelopes to strengthen the well-known second-order cone (SOC) relaxation of the ACOPF problem. With this improved relaxation, we can further include tight bounds on the voltages at the reference bus, and this paper demonstrates the effectiveness of this for improved bounds tightening. We present results on the optimality gap of both the base SOC relaxation and our Strengthened SOC (SSOC) relaxation for the National Information and Communications Technology Australia (NICTA) Energy System Test Case Archive (NESTA). For the cases where the SOC relaxation yields an optimality gap more than 0.1 %, the SSOC relaxation with bounds tightening further reduces the optimality gap by an average of 67 % and ultimately reduces the optimality gap to less than 0.1 % for 58 % of all the NESTA cases considered. Stronger relaxations enable more efficient global solution of the ACOPF problem and can improve computational efficiency of MINLP problems with AC power flow constraints, e.g., unit commitment.
O'Neill, Richard P.; Castillo, Anya; Eldridge, Brent; Hytowitz, Robin B.
The challenge to create efficient market clearing prices in centralized day-ahead electricity markets arises from inherent nonconvexities in unit commitment problems. When this aspect is ignored, marginal prices may result in economic losses to market participants who are part of the welfare maximizing solution. In this essay, we present an axiomatic approach to efficient prices and cost allocation for a revenue neutral and nonconfiscatory day-ahead market. Current cost allocation practices do not adequately attribute costs based on transparent cost causation criteria. Instead we propose an ex post multipart pricing scheme, which we refer to as the dual pricing algorithm. Our approach can be incorporated into current day-ahead markets without altering the market equilibrium.
Grid resilience is a concept related to a power system's ability to continue operating and delivering power even in the event that low probability, high-consequence disruptions such as hurricanes, earthquakes, and cyber-attacks occur. Grid resilience objectives focus on managing and, ideally, minimizing potential consequences that occur as a result of these disruptions. Currently, no formal grid resilience definitions, metrics, or analysis methods have been universally accepted. This document describes an effort to develop and describe grid resilience metrics and analysis methods. The metrics and methods described herein extend upon the Resilience Analysis Process (RAP) developed by Watson et al. for the 2015 Quadrennial Energy Review. The extension allows for both outputs from system models and for historical data to serve as the basis for creating grid resilience metrics and informing grid resilience planning and response decision-making. This document describes the grid resilience metrics and analysis methods. Demonstration of the metrics and methods is shown through a set of illustrative use cases.
The purpose of this paper is to explain some aspects of including a marginal line loss approximation in the DCOPF. The DCOPF optimizes electric generator dispatch using simplified power flow physics. Since the standard assumptions in the DCOPF include a lossless network, a number of modifications have to be added to the model. Calculating marginal losses allows the DCOPF to optimize the location of power generation, so that generators that are closer to demand centers are relatively cheaper than remote generation. The problem formulations discussed in this paper will simplify many aspects of practical electric dispatch implementations in use today, but will include sufficient detail to demonstrate a few points with regard to the handling of losses.